6 Cost of Capital

Every action of the firm takes financial resources. Plant & Equipment need to be purchased and maintained, wages and benefits need to be paid, etc. In addition, stockholders need to make a return on their investment or they will take their money elsewhere.

We saw that the process of capital budgeting was one way firms could make decisions that contribute to the wealth and return to stockholders. The capital budgeting process required as inputs, the cash-flows of the project and the firm’s cost-of-capital. In the capital budgeting unit we took each of these inputs as given. In this unit, we will take the cash-flows as given, but examine closer where firms obtain capital and the cost of each source of capital.

Firms raise capital (“get money”) using four broad categories of actions. These were illustrated in the capital budgeting unit, but are shown again here for convenience.

From the figure, we see that the firm can obtain funding from four broad sources

From bank loans.

From issuing bonds (borrowing)

From selling stock (selling ownership in the company)

From past profits (reinvesting firm profits)

Each of these four sources involves a different process, is treated differently for tax purposes, and imposes a different cost on the company.

Let’s consider a simple example.

Your firm would like to expand its operations to include Europe. This expansion will include the construction of a factory and management offices in France. The cost to initiate the expansion will be $2,000 million.

As the Chief Financial Officer (CFO) it’s your responsibility to raise the $2,000 million. The financing cost of the $2,000 million will depend on which (and how much) of the four sources of capital you decide to use.

The amount of each type of funding you decide to use is known as the capital structure. The capital structure is just the percentage of each financing source you decide to use to provide funding for your firm in general or for a specific project. For example, let’s say that you will raise the $2,000 million with $1,000 million from the sale of bonds, $100 million from the sale of preferred stock, $600 million from the sale of new stock and $300 million from previous profits. Based on these decisions, your capital structure would be ½ debt and ½ various forms of equity.

We will take the capital structure as a given in our analysis of the cost of capital.

Watch the following video to gain insight into the cost of capital structure.



6.1 The Cost of Debt

Let’s get an estimate of how much it would cost your firm to finance $1000 using debt. Based on your firm’s past financing activity, your company has a bond held by investors with the following features.

Maturity = 5 years remaining
Face Value = $1,000
Coupon Rate = 4%
Semiannual Coupons

Based on the financial health of your firm, investors are willing to pay $990 (this is just given in the problem) for that bond. By being willing to pay $990 for this bond, investors are indicating the rate of return they require to invest in your company’s bonds. The required rate on your bonds (or the cost of bond financing) is indicated by the YTM of the bond, which you know how to calculate.

We estimate the cost of bond financing by calculating the bond’s YTM.

For this bond we have:

  • N = 10 (5 years x2)

  • PV = -$990 (remember we have to make this negative when we’re solving for I/Y)

  • PMT = $20 (0.40 x $1,000 / 2)

  • FV = $1,000

  • I/Y = ? = 2.112% (make special note that this is a semi-annual rate)

  • The YTM is thus 4.224% (2.112% x 2)

You will use 4.224% as the pre-tax cost of debt. Why pre-tax?

Under current (2018) regulations, interest paid on debt is an income tax deductible expense for companies. We will come back to this distinction when we tabulate the final cost-of-capital for the firm.

6.2 The cost of equity

From the dashed box in Figure 1, we see that there are different types of equity. Let’s first look at funds raised from selling stock. Here we will include two types.

  1. Preferred Stock

  2. Commons Equity

Preferred Stock

Preferred stock is a type of ownership claim in a company that is sometimes considered a hybrid between bonds and stock. While the exact features of a share of preferred stock can vary with the company, here are some typical features of preferred stock.

Has a fixed dividend

Generally, when preferred stock is sold the dividend is set and the preferred shares are expected to pay that dividend (the preferred dividend) forever. As a consequence, we can use the perpetuity formula to calculate the price of preferred shares or, given the preferred share price, find the financing cost of preferred shares.

Preferred dividends must be paid prior to common stock dividends

While it is legal for a firm to not pay a preferred dividend on a scheduled date, if the firm misses a preferred dividend it MUST pay the missing preferred dividend before it pays the common stockholders a dividend.

Preferred shareholders have claims to firm assets after debt holders but before common stockholders

If the firm goes bankrupt or voluntarily goes out-of-business the firm must pay its liabilities to the debt holders prior to paying anything to the preferred shareholders. The preferred shareholder, however, get paid prior to the common stockholders.

Usually does not have voting rights

One “cost” of having priority over common stockholders when it comes to paying dividends or liquidating the firm’s assets, is the lack of voting rights. Preferred shareholders do not get to vote for the Board of Directors or regarding Mergers and Acquisitions.

Preferred dividends are NOT income tax deductible under current (2018) US tax laws.

While a preferred dividend is fixed and in some ways resembles a coupon payment on a bond, preferred dividends are NOT treated as interest and CANNOT be treated as a tax deductible expense.

Cost of Preferred Stock

Cost of Preferred Stock

As mentioned above, preferred stock can be treated as a perpetuity, which implies that the price of a preferred share is so that the financing cost of preferred stock is equal to [NOTE! CHECK THE TEXT ABOVE! LOOKS STRANGE, BUT IT’S THE SAME IN BOOK PDF]

\[ R_{P_{stock}} = \frac{D_pref}{P_{p_{stock}}} \]

Continuing with our example above, in the past your firm had issued preferred stock with a preferred dividend of $50.00. Based on the financial health of your firm and the legal characteristics of preferred stock, investors are willing to pay $957 (this is just given in the problem) for each share of preferred stock. Consequently, the financing cost of preferred stock for your firm is

\[ R_{P_{stock}} = \left(\frac{\$50}{\$957}\right)\times100\%=5.2247\% \]

Common Equity

Common equity is the third type of financing we will consider. Here we have two sub-categories: when the firm issues new shares of stock and when the firm reinvests profits back into the company.

New Shares

When a firm issues (sells) new shares of stock at least two cases are possible

  1. This is the first time the company has issued stock to the public. We call this an Initial Public Offering (IPO),

  2. The company has previously issued stock and this is an additional sale of stock. We call this a Seasoned Offering.

When a company wants to issue new shares of stock it will generally work with an Investment Bank that will assist the company with the legal, accounting and marketing aspects of selling stock to the public. Not surprisingly, there is a cost associated with these services. For our purposes we will lump all of these costs into what we will call “flotation costs”, which we will denote by the symbol \(F^\$\).

To estimate the financing costs of new equity we can exploit the Gordon Model we learned earlier with a slight modification. You remember that the Gordon Model state that the price of a stock is equal to

\[ P_{{common\;stock}_0}=\left( \frac{D_{common_{1}}}{R_{C_{stock}}-g} \right) \]

We can use this relation to solve for the cost of equity

\[ R_{C_{stock}}=\left( \frac{D_{common_{1}}}{P_{S\_common}} \right)+g \] When the investment bank sells the stock on behalf of the firm, it will take part of the proceeds as the flotation costs. For example, say the investment bank sells the stock for $85 per share, but its flotation costs are $2 per share. The firm would only receive $83. We can modify the equation above to account for this mechanism as:

\[ R_{C_{stock}}=\left( \frac{D_{common_{1}}}{P_{S\_common}-F^$} \right)+g \]

With this modification we can continue with our example and find the cost of newly issued stock.

The company issues new shares and the investing public believes that with the new European facilities, the company will pay a dividend of $3 next year and the dividends will grow into the distant future at a rate of 3%. As a result of this analysis, investors are willing to pay $75 (this is just given in the problem) for each share of the common equity. The investment bank’s flotation costs are $2 so we have the financing cost of common equity as

\[ R_{C_{stock_{new}}}=\left( \frac{\$3.00}{\$75-\$2} \right)+0.03= 7.11\% \]

Finally, we need to consider the cost of the profits that are reinvested in the company. When a firm has profits it essentially has two choices of what it can do with them:

  1. pay the profits to the stockholders as a dividend,

  2. invest the profits back into the company (reinvest the profits).

When the firm decides to reinvest the profits, these funds are not “free,” but impose an OPPORTUNITY cost on the firm. By deciding to reinvest the money in the firm, the stockholders do not have this money to invest on their own, so the investors are counting on the firm to earn at least as much as if the stockholders were to purchase additional shares of the firm.

The cost of reinvested funds is thus equal to the required rate of return on equity, but without the flotation costs, since the firm already has the funds.

The cost of reinvested funds is thus equal to the required rate of return on equity, but without the flotation costs, since the firm already has the funds. With this in mind, the cost is equal to

\[ R_{C_{stock}}=\left( \frac{D_{common_{1}}}{P_{S\_common}} \right)+g \]

or for our particular case

\[ R_{C_{stock}}=\left( \frac{\$3.00}{\$75} \right)+0.03 \rightarrow 7.00\% \]

The last piece of information we need to calculate our firm’s cost-of-capital is its income tax rate. We’ll assume this is 22%.

We now have all of the piece we need to calculate the firm’s weighted average cost-of-capital (WACC) for our firm.

Column 4 gives the capital structure for our firm (this is just given in the problem). Column 5 summarizes the cost of each possible way we have used to fund our company. In column 5, the figures are all pre-tax items.

Column 6 gives the after-tax costs of each of the financing sources. You will notice that except for bonds (debt) the pre-tax and after-tax values are the same for all of the financing sources. This is just a result of the particular tax laws that currently (2018) exist in the US.

Since interest on debt is income tax deductible, the after-tax cost of bond financing is

After tax cost of debt = pretax cost of debt (1 - income tax rate)

or, in this example

\[ After\;tax\;cost\;of\;debt = (4.224\%)(1-0.22)=3.2947\% \] Column 7 gives the weighted after-tax financing source costs of each financing method.

These figures are obtained by multiplying the numbers in column 4 by the numbers in column 6. The final figure we are looking for, the weighted average cost of capital (WACC) is obtained by adding up the figures in column 7 to get 5.0916%.

This means that for every $100 we raise it ends up costing us $5.09 in financing costs and it is this 5.09% that we use as our hurdle rate or discount rate when we do capital budgeting.

To solidify the process let’s do another example.

JMG Corporation is expanding its operations into the “bake-good of the month” direct marketing. This expansion will require additional production facilities as well as distribution centers. As the CFO of JMG you estimate that you will need to raise $100 million dollars for the expansion. JMG has an income tax rate of 22% and the following capital structure:

JMG’s outstanding bond have the following terms:

  • Maturity = 10 years remaining

  • Face Value = $1,000

  • Coupon Rate = 3%

  • Semiannual Coupons

  • and are selling at a price of $995.

With this information we have that the cost of bond financing is:

YTM on the bonds equals

N= 20, PV = -$995, PMT = $15, FV = $1,000, I/Y = ? –> 1.5292%

Pre-tax cost of debt is 3.0584% (1.5292% x2)

After-tax cost of debt = 3.0584% (1-0.22) = 2.3856%

JMG’s preferred stock pays an annual dividend of $60 and is currently selling for $1,500. Therefore, the cost of preferred stock is

\[ R_{P_{stock}} = \left(\frac{\$60}{\$1500}\right)\times100\%=4.0\% \]

It won’t be selling any new common equity, but it does have common equity shares outstanding. These shares have a current dividend of $3.25 per share with dividends expected to grow at 2% forever. The current stock price for these shares is $121.

The cost of common equity is thus

\[ R_{C_{stock}}=\left( \frac{\$3.3150}{\$121} \right)+0.02 \rightarrow 4.7397\% \]

The above information is summarized in the table below along with the weighted costs and the final WACC.

Click here for: In-Class Exercise 22: Cost of Capital Calculations